Unbiased Random Threshold Networks Are Chaotic or Critical
This paper has been withdrawn.
cond-mat.dis-nn↗
arXiv subjects
Volkan Sevim
Publications and source records attributed to Volkan Sevim.
Chaotic Gene Regulatory Networks Can Be Robust Against Mutations and Noise
Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do the dynamical properties and state-space structures of networks with high and low robustness differ? Does selection operate on the global dynamical behavior of the networks? What kind of state-space structures are favored by selection? We provide damage propagation analysis and an extensive statistical analysis of state spaces of these model networks to show that the change in their dynamical properties due to stabilizing selection for optimal phenotypes is minor. Most notably, the networks that are most robust to both mutations and noise are highly chaotic. Certain properties of chaotic networks, such as being able to produce large attractor basins, can be useful for maintaining a stable gene-expression pattern. Our findings indicate that conventional measures of stability, such as the damage-propagation rate, do not provide much information about robustness to mutations or noise in model gene regulatory networks.
q-bio.MN↗
Are Genetically Robust Regulatory Networks Dynamically Different from Random Ones?
We study a genetic regulatory network model developed to demonstrate that genetic robustness can evolve through stabilizing selection for optimal phenotypes. We report preliminary results on whether such selection could result in a reorganization of the state space of the system. For the chosen parameters, the evolution moves the system slightly toward the more ordered part of the phase diagram. We also find that strong memory effects cause the Derrida annealed approximation to give erroneous predictions about the model's phase diagram.
q-bio.MN↗
Network Growth with Preferential Attachment for High Indegree and Low Outdegree
We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in food-web language, number of prey) and low outdegree (or number of predators). This scheme, which we call inverse preferential attachment, is intended to maximize the amount of resources available to each new node. We show that the outdegree (predator) distribution decays at least exponentially fast for large outdegree and is continuously tunable between an exponential distribution and a delta function. The indegree (prey) distribution is poissonian in the large-network limit.
cond-mat.stat-mech↗
An individual-based predator-prey model for biological coevolution: Fluctuations, stability, and community structure
We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size fluctuations, and it generates a sequence of quasi-steady communities in the form of simple food webs. These communities are quite resilient toward the loss of one or a few species, which is reflected in different power-law exponents for the durations of communities and the lifetimes of species. The exponent for the former is near -1, while the latter is close to -2. Statistical characteristics of the evolving communities, including degree (predator and prey) distributions and proportions of basal, intermediate, and top species, compare reasonably with data for real food webs.
q-bio.PE↗
Effects of Preference for Attachment to Low-degree Nodes on the Degree Distributions of a Growing Directed Network and a Simple Food-Web Model
We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with probability proportional to 1/k_i, where k_i is the number of outgoing links at i. We calculate the degree distribution for the outgoing links in the asymptotic regime (t->infinity), both analytically and by Monte Carlo simulations. The distribution decays like k c^k/Gamma(k) for large k, where c is a constant. We investigate the effect of this preferential-attachment scheme, by comparing the results to an equivalent growth model with a degree-independent probability of attachment, which gives an exponential outdegree distribution. Also, we relate this mechanism to simple food-web models by implementing it in the cascade model. We show that the low-degree preferential-attachment mechanism breaks the symmetry between in- and outdegree distributions in the cascade model. It also causes a faster decay in the tails of the outdegree distributions for both our network growth model and the cascade model.
cond-mat.stat-mech↗
Effects of correlated interactions in a biological coevolution model with individual-based dynamics
Models of coevolution have recently been studied, in which a species is defined by a genome in the form of a bitstring, and the interactions between species i and j are given by a fixed matrix with independent, randomly distributed elements M_{ij}. A consequence of the stochastic independence is that species whose genotypes differ even by a single bit may have completely different phenotypes. This is clearly unrealistic, as closely related species should be similar in their interactions with the rest of the ecosystem. Here we therefore study a model, in which the M_{ij} are correlated to a controllable degree. We calculate, both analytically and numerically, the correlation function for matrix elements M_{ij} and M_{kl} versus the Hamming distance between the bitstrings representing the species. We compare Monte Carlo simulations of coevolution models with uncorrelated and correlated interactions. In particular, we consider the lifetimes of individual species. The species-lifetime distribution is close to a power law with an exponent near -2 in both uncorrelated and correlated cases. The durations of quasi-steady states and power spectral densities for the diversity indices display noticeable differences. However, some qualitative features, like 1/f behaviour in power spectral densities for the diversity indices, are not affected by the correlations in the interaction matrix.
q-bio.PE↗
A Biological Coevolution Model with Correlated Individual-Based Dynamics
We study the effects of interspecific correlations in a biological coevolution model in which organisms are represented by genomes of bitstrings. We present preliminary results for this model, indicating that these correlations do not significantly affect the statistical behavior of the system.
q-bio.PE↗
Evolutionary route to diploidy and sex
Using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust, that even the accidental conversion and pairing of only two diploids give rise to a sexual population.
cond-mat.soft↗
Strategies for the evolution of sex
We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multi-stable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the asexual population.
cond-mat.soft↗
Testing a hypothesis for the evolution of sex
An asexual set of primitive bacteria is simulated with a bit-string Penna model with a Fermi function for survival. A recent hypothesis by Jan, Stauffer and Moseley on the evolution of sex from asexual cells as a strategy for trying to escape the effects of deleterious mutations is checked. This strategy is found to provide a successful scenario for the evolution of a stable macroscopic sexual population.
cond-mat.soft↗